David Heron 
TABLE III. 
Showing the Comparative Values of Q, the Coefficient of Association, r, the Actual 
Correlation and Q', Mr Yule's " Theoretical Value of r," for Various Values 
of h = k. 
h = k 
Q 
r 
Q' 
Q 
r 
Q' 
Q 
r 
Q 
h=k 
Q 
r 
Q' 
0 
•13 
•10 
•06 
•37 
■30 
•19 
■60 
•50 
■33 
0 
■95 
•90 
■71 
•522 
■14 
■10 
•06 
•39 
•30 
•18 
■62 
•50 
•32 
■60 
■95 
•90 
•70 
1 -032 
•1G 
•10 
•05 
•45 
■30 
•15 
•67 
•50 
•28 
1-00 
•96 
•90 
•68 
1-635 
•22 
■10 
•03 
•56 
■30 
•10 
•77 
•50 
•21 
1-50 
•97 
■90 
•63 
2-512 
•36 
•10 
•01 
•76 
•30 
•04 
■91 
•50 
•10 
2 
•99 
•90 
•58 
3-090 
•48 
•10 
•00 
■88 
•30 
•01 
•97 
•50 
•05 
3 
1-00 
•90 
•44 
3-5 
•57 
■10 
•00 
•93 
•30 
•01 
■99 
•50 
•03 
4 
•67 
•10 
•00 
■97 
■30 
•00 
1-00 
•50 
■01 
5 
•84 
•10 
•00 
As a further example of the differences between Mr Yule's coefficient of 
association, his "theoretical value of r" and the actual value of r, I have taken 
a constant value of h = k = 3 - 09, and have plotted the curves Qx = ry and Q'x = ry 
for all values of r. Now it is clear that if R be any coefficient which is taken 
as a substitute for the correlation coefficient, then the more closely the curve 
Rx = ry approaches the line x = y the better will be the approximation to the 
true value of the correlation. I have given these curves in Fig. 6, and it is obvious 
that Q and Q' are the same as r only when r = — 1,0, and + 1, and over the whole 
range they differ so widely from r as to be absolutely useless as approximations. 
Further we see from the examples given that the curves for the coefficient of 
association for different values of h = k asymptote to the line y—1, whatever be 
the value of r ; while the curves for Mr Yule's " theoretical value of r " asymptote 
to the line y = 0. Thus we have only to take sufficiently high values of h and k 
to get either 1 or 0 as our measure of the intensity of correlation. The first 
example given, in which either - 92 or - 02 could be obtained as the measure of the 
closeness of association between deaf-mutism and imbecility is a striking illus- 
tration of this fact. 
It is unfortunate that Mr Yule has refrained from giving any example of the 
use of the second coefficient, Q, but he has made the most extensive use of the 
first, the coefficient of association. His paper " On the Association of Attributes 
in Statistics " is based on nearly 500 coefficients of association. Yet such 
coefficients are, as we have just seen, relatively as well as absolutely worthless, 
unless the material is always divided in the same proportions, and even in this 
case a number of coefficients of association are not strictly comparable since 
a small increase in the actual correlation will be followed by a large increase in 
